SUPREMUM DISTRIBUTION OF BESSEL PROCESS OF DRIFTING BROWNIAN MOTION

被引：0

作者：

Pyc, Andrzej ^{[1
]}

Serafin, Grzegorz ^{[1
]}

Zak, Tomasz ^{[1
]}

机构：

[1] Wroclaw Univ Technol, Inst Math & Comp Sci, Wybrzeze Wyspianskiego 27, PL-50370 Wroclaw, Poland

来源：

PROBABILITY AND MATHEMATICAL STATISTICS-POLAND | 2015年 / 35卷 / 02期

关键词：

Drifting Brownian motion; Bessel process; supremum distribution; estimates of theta function;

D O I：

暂无

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let us assume that (B-t((1)), B-t((2)), B-t((3)) + mu t) is a threedimensional Brownian motion with drift mu, starting at the origin. Then X-t = vertical bar vertical bar (B-t((1)), B-t((2)), B-t((3)) + mu t) vertical bar vertical bar, its distance from the starting point, is a diffusion with many applications. We investigate the supremum of (X-t), give an infinite- series formula for its distribution function and an exact estimate of the density of this distribution in terms of elementary functions.

引用

页码：201 / 222

页数：22

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